Information-theoretic Analysis of MAXCUT Algorithms

NP-hard combinatorial optimization algorithms are often characterized by their approximation ratios. In real world applications, the resilience of algorithms to input fluctuations and to modelling errors pose important robustness requirements. This work suggests a provable algorithmic regularization and validation strategy based on posterior agreement. The strategy regularizes algorithms and ranks them according to the informativeness of their output given noisy input. To illustrate this strategy, we develop methods to evaluate the posterior distribution of the Goemans-Williamson's MAXCUT algorithm using semidefinite programming relaxation (MAXCUT-SDP, [1]). Experimental comparison with typical greedy MAXCUT algorithms shows that MAXCUT-SDP with the best known approximation ratio generalizes worse than greedy MAXCUT algorithms under high noise level.